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 A005785 Number of 5-covers of an n-set. (Formerly M3949) 6
 1, 5, 28, 156, 863, 4571, 22952, 108182, 477136, 1969270, 7625579, 27804973, 95858868, 313747418, 978734539, 2920530663, 8363945469, 23057872913, 61357278239, 157985305473, 394486861086, 957156158394, 2260761331227 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Stefano Spezia, Table of n, a(n) for n = 0..10000 R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152. Vladeta Jovovic, Binary matrices up to row and column permutations Index entries for linear recurrences with constant coefficients, signature (7, -17, 13, 7, -11, 16, -44, 43, -65, 82, 46, -36, -28, -175, 85, -168, 504, 91, 77, -394, -664, -52, -382, 1642, 600, 813, -1209, -1632, -1650, -1050, 2982, 2124, 3592, -1360, -2074, -5329, -3607, 1970, 3608, 7640, 1778, 426, -8168, -6638, -3524, 2095, 8401, 6077, 5907, -5907, -6077, -8401, -2095, 3524, 6638, 8168, -426, -1778, -7640, -3608, -1970, 3607, 5329, 2074, 1360, -3592, -2124, -2982, 1050, 1650, 1632, 1209, -813, -600, -1642, 382, 52, 664, 394, -77, -91, -504, 168, -85, 175, 28, 36, -46, -82, 65, -43, 44, -16, 11, -7, -13, 17, -7, 1). FORMULA G.f.: - (x^68 - 2*x^67 + 10*x^66 + 32*x^65 + 175*x^64 + 794*x^63 + 3441*x^62 + 13186*x^61 + 46027*x^60 + 146118*x^59 + 427347*x^58 + 1155432*x^57 + 2912873*x^56 + 6875608*x^55 + 15281029*x^54 + 32094658*x^53 + 63945531*x^52 + 121210914*x^51 + 219194198*x^50 + 378998758*x^49 + 627863648*x^48 + 998282344*x^47 + 1525746624*x^46 + 2244502676*x^45 + 3181886869*x^44 + 4351201210*x^43 + 5744918381*x^42 + 7328807372*x^41 + 9039504349*x^40 + 10785767638*x^39 + 12455264802*x^38 + 13925287384*x^37 + 15077477135*x^36 + 15812782150*x^35 + 16065602576*x^34 + 15812782150*x^33 + 15077477135*x^32 + 13925287384*x^31 + 12455264802*x^30 + 10785767638*x^29 + 9039504349*x^28 + 7328807372*x^27 + 5744918381*x^26 + 4351201210*x^25 + 3181886869*x^24 + 2244502676*x^23 + 1525746624*x^22 + 998282344*x^21 + 627863648*x^20 + 378998758*x^19 + 219194198*x^18 + 121210914*x^17 + 63945531*x^16 + 32094658*x^15 + 15281029*x^14 + 6875608*x^13 + 2912873*x^12 + 1155432*x^11 + 427347*x^10 + 146118*x^9 + 46027*x^8 + 13186*x^7 + 3441*x^6 + 794*x^5 + 175*x^4 + 32*x^3 + 10*x^2 - 2*x + 1)/((x^6 - 1)^2*(x^4 + x^3 + x^2 + x + 1)^6*(x^3 - x^2 + x - 1)^6*(x^2 + x + 1)^6*(x + 1)^10*(x - 1)^23). a(n) = n^30/(30!*5!) + O(n^29). - Vaclav Kotesovec, Aug 09 2022 CROSSREFS Cf. A052264, A002620, A005783, A005784, A055066. Sequence in context: A164537 A015536 A271808 * A027912 A243669 A327999 Adjacent sequences: A005782 A005783 A005784 * A005786 A005787 A005788 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Jun 03 2000 a(0) = 1 prepended by Stefano Spezia, Aug 09 2022 STATUS approved

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Last modified February 1 04:32 EST 2023. Contains 359981 sequences. (Running on oeis4.)